Question

Given statements are based on Bohr's atomic model for hydrogen-like atoms

Statement 1: As the principal quantum number increases, the speed of the electron also increases.

Statement 2: Speed of electron increases as energy increases.

• A. Both statement 1 and statement 2 are true
• B. Only statement 1 is true
• C. Only statement 2 is true
• D. Both statement 1 and statement 2 are false

Answer 1

The correct option is D

Both statement 1 and statement 2 are false

Explanation for correct option:

The principal quantum number is denoted by $\mathrm{n}$.

$\mathrm{V}={\mathrm{V}}_0\frac{\mathrm{Z}}{\mathrm{n}}$

As we can see, principal quantum number $\mathrm{n}$ is inversely proportional to the velocity. Therefore, if $\mathrm{n}$ increases, velocity will decrease.

To calculate the energy of electrons, we use the formula:

$\mathrm{E}=\frac{-13.6{\mathrm{Z}}^2}{{\mathrm{n}}^2}$

As we can see, principal quantum number $\mathrm{n}$ is inversely energy proportional to the energy. Therefore, if $\mathrm{n}$ increases, energy will decrease.

Hence option (D) is the correct option.